Strong Correlations and Topology: new frontiers and emerging interconnections

Our current understanding of topological materials might be likened to that  of Bose–Einstein condensation (BEC) prior to the discovery of

superfluidity.  Whereas theory predicts BEC in a non-interacting Bose gas, interactions are required to stabilize superfluidity.  In a similar fashion,  topological properties are predicted for non-interacting topological insulators, but interactions will likely induce additional collective phenomenon. 

I shall review some of the current mysteries of strongly correlated topology, focussing particularly on the case of Kondo insulators and Superconductors.  As a concrete example of a challenging new developments, I will present some recent tunneling results that demonstrate that the strange topological Kondo Insulator Samarium Hexaboride undergoes an axionic phase transition at low temperatures - with a surface spin magnetization proportional to an applied electric field[1].  In particular, I  will discuss how the Kondo effect at the surface of topological Kondo insulators may lead to surface time-reversal symmetry breaking, while preserving the metallic surface states.